Prime numbers are those numbers divisible only by itself and one. For centuries mathematicians calculated them hoping to make some kind of a breakthrough that might prove them to be useful. A Mersenne prime is a prime number that is also all ones in binary (3 is 11 binary, 7 is 111, etc.) Up until the 19th century, there was little use for either flavor of prime numbers, and calculating these numbers was a purely mathematical exercise until cryptographers discovered how to use them to create nearly unbreakable codes.
It was found that using two prime numbers multiplied together makes a much better encryption key than any random number, because the product has only three factors. Large prime numbers (hundreds or thousands of places long) are exceedingly hard to factor and cryptographic keys derived from them are likewise computationally infeasible to crack.
What relevance does this have to your personal computer, your Mac or PC? Please be patient, I am getting there.Ancient mathematicians knew of the first few Mersenne prime numbers 1, 3, 7, 13, and 31, but it was not until 1461 that the sixth one was found. Even using modern computers there are only 42 Mersenne to have been discovered, and of these 13 (also a prime number) have been discovered in the last dozen years by a distributed computer project named The Great Internet Mersenne Prime Search.
GIMPS is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers. The project has found a total of fourteen Mersenne primes as of 5 February 2013. The last one discovered has 12,978,189 digits and to understand why I do not print that number here in this column you need to realize doing so would require some 3,000 pages (I am allotted about half of a page per week and at that rate it would take me 115 years to print the complete number). That is one big number!
GIMPS makes available for download the free software that allows anyone, you or me, to join the search for the next Mersenne prime. There are some fiduciary incentives for doing this in the form of cash awards for being the one who discovers the next Mersenne prime number. 100,000 dollars was awarded for discovery of the first 10 million digit prime number, and a larger prize awaits the person whose computer discovers the first verified 100 million digit Mersenne prime.
So, is that the reason I am writing this, to urge everyone to do this? Not really, your odds of winning the lottery are a whole lot better, but thanks for being patient and I will now get to the point of this column:
Shortly after GIMPS came into existence in 1995, some of the people who participated in the search for new prime numbers by downloading and installing the Prime95 software found that it caused their computers to crash. It seems that crunching large multi-million-digit numbers is a formidable task that requires 100% of your computer’s resources to be in absolutely top condition or it will crash under the load. Computer technicians jumped on this right away and Prime95 quickly became a popular way to test computers under maximum possible stress. A computer system that might seem to work okay under the minimal load of using a word processor or while surfing the web might have defective hardware that simply does not manifest itself under normal usage. Factoring some of those gigantic numbers is more likely to reveal any hardwire defect that exists in your computer.
The next time your Mac or PC is behaving badly and you want to know if the problem is hardware or software, just download a copy of Prime95 and let it run for a few days. If your computer survives such a workout then its CPU and RAM are probably okay. Maybe your computer could be the next to discover a new Mersenne prime and win a cash research award.
Reporter contributor Charles Miller is a freelance computer consultant with more than 20 years IT experience and a Texan with a lifetime love for Mexico. The opinions expressed are his own. He may be contacted through his web site at SMAguru.com.